The coefficient of static and kinetic friction between the two blocks and also between the lower block and the ground are ${\mu }_s=0.6$ and ${\mu }_k=0.4$. Find the value of tension T (in N) applied on the lower block at which the upper block begins to slip relative to lower block. 

The maximum static friction on upper block and lower block is $f1\text{ max}=\mu \text{Sm}1\text{ g}=0.6$ $2\times 10=12\text{ N}$ The maximum static friction between ground and lower block is$F2 \text{max}=\mu \text{S}(\text{m}1+\text{m}2)\text{g}=0.6\times 4\times 10=24\text{ N}$ Assume that both blocks move together.
$\begin{array}{l}T-{\mu }_k(m_1+m_2)g=(m_1+m_2)a\\ T-0.4\times 4\times 10=4a\\ \text{ or }T-16=4a\dots \left(1\right)\end{array}$

For upper block :
$\begin{array}{rr}{f}_1& =2a=2\left(\frac{T-16}{4}\right)\\ \text{ or }{f}_1& =\frac{T-16}{2}\end{array}$

For just sliding,
$\begin{array}{c}{\text{f}}_1={\text{f}}_{1\text{max}}\\ \text{ or }\frac{\text{T}-16}{2}=12\\ \text{ or }T-16=24\end{array}$
$T=24+16=40N$